We shouldn't deny the 'existence' of these problems. [=we shouldn't deny that these problems are present or real]
long before the country had 'come into existence' [=begun to exist; come to have actual being]
I owe my very 'existence' [='life'] to their courage. [=I am alive because of their courage]
(..) So... ...what do you do? - What do I do? - Mm-hm. I'm the key figure in a government plot to deny the existence of extraterrestrials. It's a global conspiracy with key players in the highest levels of power. And it reaches down into the lives of every man, woman and child on this planet. (..)1998 The X Files